Fig. 4: Two methods for thermal state preparation.
From: The phase diagram of quantum chromodynamics in one dimension on a quantum computer
Bottom left: The protocol suitable for a qubit ancilla using a CNOT gate. Right: Alternative protocol utilising a motional ancilla. The system qubit and ancillary motional mode are both in their ground states. A blue sideband transition on the qubit resonance coherently transfers population from \(\left\vert {{{\rm{qubit,\; motion}}}}\right\rangle=\left\vert 0,0\right\rangle\) to \(\left\vert 1,1\right\rangle\), resulting in the final state \(\cos (\theta /2)\left\vert 0,0\right\rangle+\sin (\theta /2)\left\vert 1,1\right\rangle\).
